Question

triangle RSt is similar to triangle xyz with rs= 3 inches and xy= 2 inches. Of the area of triangle RST is 27 in^2, determine and state the area of triangle XYZ in square inches.

Answer 1

Answer: The area of triangle ΔXYZ is 12 square inches.

Step-by-step explanation:

Since we have given that

RS = 3 inches

XY = 2 inches

Area of ΔRST = 27 in²

Since ΔRST is similar to ΔXYZ.

So, using the "Area similarity theorem":

$\dfrac{\Delta RST}{\Delta XYZ}=\dfrac{RS^2}{XY^2}\\\\\dfrac{27}{\Delta XYZ}=\dfrac{3^2}{2^2}\\\\\dfrac{27}{\Delta XYZ}=\dfrac{9}{4}\\\\\Delta XYZ=3\times 4=12\ in^2$

Hence, the area of triangle ΔXYZ is 12 square inches.