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The length of a diagonal of a rectangular park is 40 meters, and that of one of its sides is 24 meters. Find the perimeter of the park.

102 m

112 m

122 m

132 m

Correct Answer

📐 MA • Math Direct FormulaMathematicsMensuration

Option B

112 m

Quick Summary:

Recognize the Pythagorean triple (3, 4, 5). Here, $40 = 5 \times 8$ and $24 = 3 \times 8$ , so the missing side is $4 \times 8 = 32$ . Perimeter = $2(24 + 32) = 112$ .

📐MAMath SolutionDirect Formula

📋 Given

Diagonal (d) = 40 m, Length (l) = 24 m

🔢 Formula Used

d2=l2+b2d^2 = l^2 + b^2d2=l2+b2, P=2(l+b)P = 2(l + b)P=2(l+b)

⚡ Exam Hall Shortcut / Speed Trick

Recognize the Pythagorean triple (3, 4, 5). Here, $40 = 5 \times 8$ and $24 = 3 \times 8$ , so the missing side is $4 \times 8 = 32$ . Perimeter = $2(24 + 32) = 112$ .

⚠️ Common Student Trap / Pitfall

Students often misidentify the diagonal as one of the sides or calculate the area ( $l \times b$ ) instead of the perimeter ( $2(l+b)$ ).

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Calculate the unknown side (b)

Since the park is rectangular, the diagonal forms a right-angled triangle. By Pythagoras theorem, the width $b$ is $\sqrt{d^2 - l^2}$ .

b=402−242=1600−576=1024=32 mb = \sqrt{40^2 - 24^2} = \sqrt{1600 - 576} = \sqrt{1024} = 32 \text{ m}b=402−242​=1600−576​=1024​=32 m

Calculate the perimeter (P)

Substitute the length $l = 24$ and width $b = 32$ into the perimeter formula $P = 2(l + b)$ .

P=2(24+32)=2(56)=112 mP = 2(24 + 32) = 2(56) = 112 \text{ m}P=2(24+32)=2(56)=112 m

✅

B is correct because the calculated perimeter of the rectangular park is 112 m.

Core Concepts Used

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Pythagoras Theorem Rectangle Properties Perimeter Calculation

💡 EXAM TIP

Pythagorean triples are vital for Geometry; memorizing common sets like (3,4,5), (5,12,13), and (8,15,17) significantly speeds up Coordinate Geometry and Mensuration problems.

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