You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard X

Mathematics

Statement of Pythagoras' Theorem

In the given ...

Question

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

Q. 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 x = ___ and y = ___.

Q. In the given figure, BD bisects

∠ A B C

and BD is perpendicular to AC. Find x + y.

Q. If

∠ A = 100^{\circ}

, AB = AC, CD bisects

∠ A C B

and BD bisects

∠ A B C

. The values of x and y are

Q. In the given figure, if

R B, S C

and

T D

are perpendiculars to

B D

with lengths

x, z

and

y

, then the ratio of

x

and

y

is :

Join BYJU'S Learning Program

In the given figure, BD bisects ∠ABC 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.

In ΔABD and ΔCBD (i) ∠ABD=∠CBD ... (given ) (ii) BD=BD……(common) (iii) ∠BDA=∠BDC=90∘ ….(given) ∴ΔABD≅ΔCBD (ASA postulate) ⇒AD=DC ……..(CPCT) 5x–3=2x+63x=9x=3 and BA=BC ……..(CPCT) 2y–1=132y=14y=7

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.