Join 60,000+ competitive exam aspirants
or with email
Your Cart
Subtotal₹0
Total₹0
Examoogle • User • info@examoogle.com • EE-2024-8821
Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked
Join 60,000+ competitive exam aspirants
The sum of three sides of an isosceles triangle is 20 cm, and the ratio of an equal side to the base is 3:4. The altitude of the triangle is:
25 cm
33 cm
35 cm
45 cm
25 cm
Given ratio 3:4, let sides be 3x, 3x, 4x. Perimeter 3x+3x+4x = 10x = 20, so x = 2. Sides are 6, 6, 4. Altitude to base 4 splits it into 2, 2. Using Pythagoras: h = sqrt(6² - 2²) = sqrt(36 - 4) = sqrt(32)=42 cm is not an option. Re-evaluating: If 4x is base, 3x is side: 6,6,8 is impossible (perimeter 20). If 3x is base, 4x is side: 4,8,8 (perimeter 20). h = sqrt(8² - 2²) = sqrt(64 - 4) = sqrt(60)=215. Wait, checking ratio 3:4 again. 3x, 3x, 4x → 10x=20 → x=2. Sides 6, 6, 4. Altitude h = sqrt(6² - 2²) = sqrt(32)=42. Let's re-read ratio: 'equal side to the base is 3:4'. Side = 3x, Base = 4x. 3x+3x+4x = 10x = 20 => x=2. Side=6, Base=4. Altitude = sqrt(6² - 2²) = sqrt(32)=42. Actually, if Base = 3x, Side = 4x, then 4x+4x+3x = 11x = 20. If 3x = side, 4x = base, sides are 6, 6, 8 (perimeter 20). Altitude = sqrt(6² - 4²) = sqrt(20)=25.
Perimeter of isosceles triangle = 20 cm. Ratio of equal side (a) to base (b) = 3:4.
P=2a+b, h=a2−(b/2)2
Given ratio 3:4, let sides be 3x, 3x, 4x. Perimeter 3x+3x+4x = 10x = 20, so x = 2. Sides are 6, 6, 4. Altitude to base 4 splits it into 2, 2. Using Pythagoras: h = sqrt(6² - 2²) = sqrt(36 - 4) = sqrt(32)=42 cm is not an option. Re-evaluating: If 4x is base, 3x is side: 6,6,8 is impossible (perimeter 20). If 3x is base, 4x is side: 4,8,8 (perimeter 20). h = sqrt(8² - 2²) = sqrt(64 - 4) = sqrt(60)=215. Wait, checking ratio 3:4 again. 3x, 3x, 4x → 10x=20 → x=2. Sides 6, 6, 4. Altitude h = sqrt(6² - 2²) = sqrt(32)=42. Let's re-read ratio: 'equal side to the base is 3:4'. Side = 3x, Base = 4x. 3x+3x+4x = 10x = 20 => x=2. Side=6, Base=4. Altitude = sqrt(6² - 2²) = sqrt(32)=42. Actually, if Base = 3x, Side = 4x, then 4x+4x+3x = 11x = 20. If 3x = side, 4x = base, sides are 6, 6, 8 (perimeter 20). Altitude = sqrt(6² - 4²) = sqrt(20)=25.
Confusing the ratio 'equal side to base' and using the wrong side length for the Pythagorean theorem calculation.
Define sides
Given ratio of side a to base b is 3:4. Let a=3x and b=4x. Wait, if a=3x and b=4x, then 2a+b=2(3x)+4x=10x. Given perimeter is 20, so 10x=20⟹x=2. This makes the sides 6,6,8.
a=6,b=8
Calculate altitude
The altitude h to the base b bisects the base into two segments of length b/2=4. Using the Pythagorean theorem in one of the resulting right triangles:
h=a2−(b/2)2=62−42
Final computation
Subtract the squares and find the square root:
h=36−16=20=25
A is correct because the isosceles triangle with sides 6 cm, 6 cm, and 8 cm has an altitude to the 8 cm base of 2√5 cm.
Always verify triangle inequality (sum of two sides > third side) when dealing with geometric side ratios; here 6+6 > 8 holds.
Get instant step-by-step AI explanations, full shift Previous Year Papers (SSC GD, RRB, SSC JE), and regional rank analysis on the official Examoogle App.
Free Download • 100K+ Aspirants