In a triangle ABC- if AB -2 x -1- AC -2 -2 x and BC -2 x -1- Find the angle - BAC-A- 60-B- 45- 90-D- 30-

The correct option is C 90^∘ AB^2 = (2x 1)^2 = 4x^2+1 4x AC^2 = ( 2√(2x) )^2 = 8x BC^2 = (2x+1)^2 = 4x^2+1+4x We can observe here, AB^2+AC^2=4x^2+1 4x+8x ...

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

Byju's Answer

Standard X

Mathematics

Converse of Pythagoras' Theorem

In a triangle...

Question

In a triangle ABC, if AB = 2x - 1, $A C = 2 \sqrt{2 x}$ and BC = 2x + 1. Find the angle $∠ B A C$ .

$30^{\circ}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$60^{\circ}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$45^{\circ}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$90^{\circ}$

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D
$90^{\circ}$

$A B^{2} = (2 x - 1)^{2} = 4 x^{2} + 1 - 4 x A C^{2} = (2 \sqrt{2 x})^{2} = 8 x B C^{2} = (2 x + 1)^{2} = 4 x^{2} + 1 + 4 x$
We can observe here,
$A B^{2} + A C^{2} = 4 x^{2} + 1 - 4 x + 8 x = 4 x^{2} + 1 + 4 x = B C^{2}$
$A B^{2} + A C^{2} = B C^{2}$
So from converse of pythagorian theorem we have,
$∠ A = 90^{\circ}, ∠ B A C = 90^{\circ}$

Suggest Corrections

Similar questions

Q. In a triangle ABC, if AB=2x-1,

A C = 2 \sqrt{2 x}

and BC=2x+1. Find the angle

∠ B A C

In the given isosceles triangle ABC, AB = AC, $∠ A B C$ = 70°. Find $∠$ BAC.

Q. In an isosceles triangle ABC if AC = BC and AB² = 2AC², then ∠C =

(a) 30°
(b) 45°
(c) 90°
(d) 60°

In triangle ABC, AB=m²-n², BC=2mn and AC=m²+n², the value of angle ABC is-

A)90°

B)30°

C)60°

D)45°

In a $△ A B C, ∠ A = 60^{\circ}, ∠ B = 30^{\circ}$ and $∠ C = 90^{\circ} .$

Then the ratio $A C : B C : A B$ will be equal to

Join BYJU'S Learning Program

In a triangle ABC, if AB = 2x - 1, AC=2√2x and BC = 2x + 1. Find the angle ∠BAC.

The correct option is D 90∘ AB2=(2x−1)2=4x2+1−4xAC2=(2√2x)2=8xBC2=(2x+1)2=4x2+1+4x We can observe here, AB2+AC2=4x2+1−4x+8x=4x2+1+4x=BC2 AB2+AC2=BC2 So from converse of pythagorian theorem we have, ∠A=90∘, ∠BAC=90∘

In a triangle ABC, if AB = 2x - 1, $A C = 2 \sqrt{2 x}$ and BC = 2x + 1. Find the angle $∠ B A C$ .