In Delta PQR, the midpoints of the sides are | vedclass

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(A) According to the Midpoint Theorem,the triangle formed by joining the midpoints of the sides of a triangle divides the original triangle into four

Vedclass · Accepted Answer

Area of $\Delta XYZ = 60,$ Area of $\Delta ABC = 15$

Vedclass · Answer

(A) According to the Midpoint Theorem,the triangle formed by joining the midpoints of the sides of a triangle divides the original triangle into four congruent triangles,each having an area equal to $1/4$ of the original triangle.$1$. For $\Delta PQR,$ the midpoints are $X, Y, Z.$ Therefore,$	ext{Area}(\Delta XYZ) = \frac{1}{4} 	imes 	ext{Area}(\Delta PQR) = \frac{1}{4} 	imes 240 = 60.$$2$. Similarly,for $\Delta XYZ,$ the midpoints are $A, B, C.$ Therefore,$	ext{Area}(\Delta ABC) = \frac{1}{4} 	imes 	ext{Area}(\Delta XYZ) = \frac{1}{4} 	imes 60 = 15.$Thus,the area of $\Delta XYZ$ is $60$ and the area of $\Delta ABC$ is $15.$

In $\Delta PQR,$ the midpoints of the sides are $X, Y, Z.$ In $\Delta XYZ,$ the midpoints of the sides are $A, B, C.$ If the area of $\Delta PQR$ is $240,$ find the area of $\Delta XYZ$ and $\Delta ABC.$

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