12. . If area of $\vartriangle PQR$ is $9c{{m}^{2}}$ and area of $\vartriangle XYZ$ is$16c{{m}^{2}}$and if $QR=2.1cm$, find the length of YZ.

12. . If area of $\vartriangle PQR$ is $9c{{m}^{2}}$ and area of $\vartriangle XYZ$ is $16c{{m}^{2}}$ and if $QR=2.1cm$ , find the length of YZ.

Class 10 | Frank | ICSE | Maths | Similarity

12. . If area of $\vartriangle PQR$ is $9c{{m}^{2}}$ and area of $\vartriangle XYZ$ is $16c{{m}^{2}}$ and if $QR=2.1cm$ , find the length of YZ.

Given that, $\vartriangle PQR\sim \vartriangle XYZ$ , area of $\vartriangle PQR$ is $9c{{m}^{2}}$ and area of $\vartriangle XYZ$ is $16c{{m}^{2}}$ and $QR=2.1cm$

As we know that, the ratio of areas of two similar triangles is equal to the ratio of square of their corresponding sides. $Areaof\vartriangle PQR/Areaof\vartriangle XYZ=Q{{R}^{2}}/Y{{Z}^{2}}$

$9/16={{(21)}^{2}}/{{(YZ)}^{2}}$

We are Taking square root on both sides we get,

$3/4=2.1/YZ$

$YZ=\left(2.1\times 4 \right)/3$

$YZ=2.8$

Hence, YZ is $2.8cm$ .

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