Triangle ABC is similar to triangle DEF with $\frac{BC}{EF} = ... | Mathematics MCQ

MathematicsPrevious Year Paper 2024

Triangle ABC is similar to triangle DEF with $\frac{BC}{EF} = \frac{1}{4}$ . Find $\frac{\text{Area (triangle DEF)}}{\text{Area (triangle ABC)}}$ .

$\frac{1}{4}$

$16$

$\frac{1}{16}$

$4$

Correct Answer

📐 MA • Math Direct FormulaMathematicsPrevious Year Paper 2024

Option B

$16$

Quick Summary:

For similar triangles, the ratio of their areas is equal to the square of the ratio of their corresponding sides.

🎯

Crack Previous Year Paper 2024 with Examoogle SuperTeachers

Get Free Demo Classes & Live Mocks →

📐MAMath SolutionDirect Formula

📋 Given

Triangle ABC is similar to triangle DEF, and the ratio of side lengths is $\frac{\overline{BC}}{\overline{EF}}$ = $\frac{1}{4}$ .

🔢 Formula Used

Area (triangle DEF)Area (triangle ABC)=(EFBC)2\frac{\text{Area (triangle DEF)}}{\text{Area (triangle ABC)}} = \left(\frac{\text{EF}}{\text{BC}}\right)^2Area (triangle ABC)Area (triangle DEF)​=(BCEF​)2

⚡ Exam Hall Shortcut / Speed Trick

For similar triangles, the ratio of their areas is equal to the square of the ratio of their corresponding sides.

⚠️ Common Student Trap / Pitfall

Inverting the ratio order. Since the question asks for Area (triangle DEF) / Area (triangle ABC), you must square the inverse of the given side ratio $\frac{\overline{BC}}{\overline{EF}}$ .

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Recall the Area Theorem for Similar Triangles

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding side lengths.

Area (triangle DEF)Area (triangle ABC)=(EFBC)2\frac{\text{Area (triangle DEF)}}{\text{Area (triangle ABC)}} = \left(\frac{\text{EF}}{\text{BC}}\right)^2Area (triangle ABC)Area (triangle DEF)​=(BCEF​)2

Substitute the Given Values

We are given $\frac{\overline{BC}}{\overline{EF}} = \frac{1}{4}$ . Therefore, the inverse ratio is $\frac{\overline{EF}}{\overline{BC}} = \frac{4}{1} = 4$ .

EFBC=4\frac{\text{EF}}{\text{BC}} = 4BCEF​=4

Calculate the Area Ratio

Squaring the side ratio gives the final ratio of the areas.

16=(4)216 = (4)^216=(4)2

✅

B is correct because the ratio of the areas of two similar triangles is the square of the ratio of their corresponding sides, giving $4^2 = 16$ .

Core Concepts Used

Click any tag to open in AI Tutor

💡 EXAM TIP

For similar 3D solids, the ratio of their volumes is equal to the cube of the ratio of their corresponding linear dimensions ( $k^3$ ).

Was this solution helpful?

⚡ Practice on Android App · 4.8 ★

Solve 10,000+ More Questions with AI Tutor

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

Discussion (0)

Loading discussion...

Prev Next

Correct Answer

Solve 10,000+ More Questions with AI Tutor

Related Questions

Discussion (0)

Correct Answer

Solve 10,000+ More Questions with AI Tutor

Related Questions

Discussion (0)