In the given figure, BD bisects $∠ A B C$ and BD is perpendicular to AC. If the lengths of the sides of the triangle are expressed in terms of x and y as shown, then find the value of x and y.

Open in App

Solution

In $Δ A B D$ and $Δ C B D$

(i) $∠ A B D = ∠ C B D$ ... (given )

(ii) $B D = B D$ ……(common)

(iii) $∠ B D A = ∠ B D C = 90^{\circ}$ ….(given)

$∴ Δ A B D ≅ Δ C B D$ (ASA postulate)

$\Rightarrow A D = D C$ ……..(CPCT)
$5 x - 3 = 2 x + 6 3 x = 9 x = 3$

and $B A = B C$ ……..(CPCT)
$2 y - 1 = 13 2 y = 14 y = 7$

Suggest Corrections

Similar questions

In the triangle ABC, BD bisects angle B and is perpendicular to AC. If the lengths of the sides of the triangle are expressed in terms of x and y as shown, find the values of x and y.

In the given figure, BD bisects $∠ A B C$ and BD is perpendicular to AC. If the lengths of the sides of the triangle are expressed in terms of x and y as shown, then find the value of x and y. [3 Marks]

In the given figure, BD bisects $∠ A B C$ and BD is perpendicular to AC. If the lengths of the sides of the triangle are expressed in terms of x and y as shown, then x = ___ and y = ___.