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CAT 2003 Slot 2 — QA Question 1

Similarity of TrianglesEasy

A piece of paper is in the shape of a right angled triangle and is cut along a line that is parallel to the hypotenuse, leaving a smaller triangle. There was a 35% reduction in the length of the hypotenuse of the triangle. If the area of the original triangle was 34 square inches before the cut, what is the area (in square inches) of the smaller triangle?

Answer & solution

  • A

    16.665

  • B

    16.565

  • C

    15.465

  • 14.365

Solution

Since DE is parallel to AC, ∆ABC is similar to ∆DBE by AAA rule of similarity,

i.e. ΔABC ~ ΔDBE

When two triangles are similar, the ratio of their areas is equal to the ratio of squares of their corresponding sides.

∴Area(∆ABC)Area(∆DBE)=(ACDE)2=(10.65)2

∴ Area (∆DBE) = (0.65)2 × Area (∆ABC)

∴ Area (∆DBE) = 0.4225 × 34 = 14.365

Hence, option (d).

CAT 2003 Slot 2 QA Q1: A piece of paper is in the shape of a right angled triangle and is cut along a line that is parallel to the hy — Solution | TheCATExam