XY is drawn parallel to BC- the base of - ABC- If - AXY - Trapezium XBCY -4- 5 - Show that- AX - XB -2- 1-

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Standard X

Mathematics

Relation between Areas and Sides of Similar Triangles

XY is drawn p...

Question

XY is drawn parallel to BC, the base of ΔABC. If ΔAXY : Trapezium XBCY = 4:5. Show that, AX : XB = 2 : 1.

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Solution

Given: In ΔABC, BC || XY and Area (ΔAXY): Area (trapezium XBCY) = 4: 5.

Since BC||XY, ΔABC and ΔAXY are similar.

By Area theorem, the areas of two similar triangles are proportional to the squares of the corresponding sides.

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XY is drawn parallel to BC, the base of ΔABC. If ΔAXY : Trapezium XBCY = 4:5. Show that, AX : XB = 2 : 1.

Given: In ΔABC, BC || XY and Area (ΔAXY): Area (trapezium XBCY) = 4: 5. Since BC||XY, ΔABC and ΔAXY are similar. By Area theorem, the areas of two similar triangles are proportional to the squares of the corresponding sides.

Given: In ΔABC, BC || XY and Area (ΔAXY): Area (trapezium XBCY) = 4: 5.

Since BC||XY, ΔABC and ΔAXY are similar.

By Area theorem, the areas of two similar triangles are proportional to the squares of the corresponding sides.