Question : If for an isosceles triangle, the length of each equal side is $a$ units and that of the third side is $b$ units, then its area will be:
Option 1: $\frac{1}{4}\sqrt{4b^{2}-a^{2}}$ sq. units
Option 2: $\frac{a}{2}\sqrt{2a^{2}-b^{2}}$ sq. units
Option 3: $\frac{b}{4}\sqrt{4a^{2}-b^{2}}$ sq. units
Option 4: $\frac{b}{2}\sqrt{a^{2}-2b^{2}}$ sq. units

Question

Question : If for an isosceles triangle, the length of each equal side is $a$ units and that of the third side is $b$ units, then its area will be:

Option 1: $\frac{1}{4}\sqrt{4b^{2}-a^{2}}$ sq. units

Option 2: $\frac{a}{2}\sqrt{2a^{2}-b^{2}}$ sq. units

Option 3: $\frac{b}{4}\sqrt{4a^{2}-b^{2}}$ sq. units

Option 4: $\frac{b}{2}\sqrt{a^{2}-2b^{2}}$ sq. units

Team Careers360 · Accepted Answer

Correct Answer: $\frac{b}{4}\sqrt{4a^{2}-b^{2}}$ sq. units

Solution :
In an isosceles triangle with two sides of length $a$ units and a base of length $b$ units.
The height can be found using the Pythagorean theorem,
$ = \sqrt{a^2 - \left(\frac{b}{2} ight)^2}$
The area of the triangle,
$= \frac{1}{2} imes$ base $ imes$ height
$= \frac{1}{2} imes b imes \sqrt{a^2 - \left(\frac{b}{2} ight)^2}$
$= \frac{1}{2} imes b imes \sqrt{a^2 - \left(\frac{b^2}{4} ight)}$
$= \frac{1}{2} imes b imes \sqrt{\left(\frac{4a^2-b^2}{4} ight)}$
$= \frac{1}{4} imes b imes \sqrt{(4a^2-b^2)}$
$= \frac{b}{4} imes \sqrt{(4a^2-b^2)}$
Hence, the correct answer is $ \frac{b}{4} imes \sqrt{(4a^2-b^2)}$ sq. units.

Exams

Colleges

Predictors

Resources

Quick links

Exams

Colleges & Courses

Predictors

Resources

Exams

Colleges

Predictors & E-Books

Resources

Engineering Preparation

Medical Preparation

Law Preparation

MBA Preparation

Exams

Colleges

Resources

Exams

Colleges

Predictors & Articles

Resources

Exams

Colleges

Predictors

Resources

Exams

Colleges

Upcoming Events

Resources

Exams

Colleges

Resources

Quick Links

Top Streams

Specializations

Resources

Top Providers

Exams

Colleges

Resources

Diploma Colleges

Exams

Colleges

Resources

Exams

Resources

Top Courses & Careers

Colleges

Exams

Upcoming Events

Resources

Other Exams

Exams

Colleges

Top Countries

Resources

Exams

Top Schools

Products & Resources

NCERT Study Material

Question : If for an isosceles triangle, the length of each equal side is a units and that of the third side is b units, then its area will be:Option 1: 144b2−a2 sq. unitsOption 2: a22a2−b2 sq. unitsOption 3: b44a2−b2 sq. unitsOption 4: b2a2−2b2 sq. units

Related Questions

Know More about

Upcoming Exams

Trending Articles around SSC CGL

Download the Careers360 App on your Android phone

Sign In/Sign Up