Question : The altitude drawn to the base of an isosceles triangle is 8 cm and its perimeter is 64 cm. The area (in cm2) of the triangle is:
Option 1: 240
Option 2: 180
Option 3: 360
Option 4: 120
Recommended: How to crack SSC CHSL | SSC CHSL exam guide
Don't Miss: Month-wise Current Affairs | Upcoming government exams
New: Unlock 10% OFF on PTE Academic. Use Code: 'C360SPL10'
Correct Answer: 120
Solution : Let the base of the isosceles triangle as $b\operatorname{ cm }$ and each of the equal sides as $a\operatorname{ cm }$. The altitude drawn to the base = $8\operatorname{ cm }$ The perimeter of the isosceles triangle = $64\operatorname{ cm }$ In an isosceles triangle, the altitude bisects the base, dividing it into two equal parts. Let each part as $\frac{b}{2}$. We can use the Pythagorean theorem, $⇒a = \sqrt{(\frac{b}{2})^2 + 8^2}$ ____(i) Given that the perimeter of the triangle is $64\operatorname{ cm }$. $⇒2a + b = 64$ ____(ii) From equation (i) and equation (ii), $⇒2\sqrt{(\frac{b}{2})^2 + 8^2} + b = 64$ $⇒\sqrt{ b^2 + 256}=64-b$ $⇒b^2 + 256=4096-128b+b^2$ $⇒128b=3840$ $⇒b = 30\operatorname{ cm }$ From equation (ii), $⇒a = 17\operatorname{ cm }$. The area of the triangle $=\frac{1}{2}bh=\frac{1}{2} \times 30 \times 8 = 120\operatorname{ cm^2 }$ Hence, the correct answer is 120.
Candidates can download this e-book to give a boost to thier preparation.
Application | Eligibility | Admit Card | Answer Key | Preparation Tips | Result | Cutoff
Question : The length of the base of a triangle is 10 cm and its altitude from the same base is 8 cm. What is the area of the triangle?
Option 1: 30 cm2
Option 2: 40 cm2
Option 3: 50 cm2
Option 4: 80 cm2
Question : If the altitude of a triangle is 8 cm and its corresponding base is 12 cm, then the area of the triangle will be:
Option 1: 96 cm2
Option 2: 48 cm2
Option 3: 84 cm2
Option 4: 24 cm2
Question : In an isosceles triangle, if the unequal side is 8 cm and the equal sides are 5 cm, then the area of the triangle is:
Option 1: 12 cm2
Option 2: 25 cm2
Option 3: 6 cm2
Option 4: 11 cm2
Question : If the altitude of a right prism is 10 cm and its base is an equilateral triangle of side 12 cm, then its total surface area (in cm2) is:
Option 1: $(5+3\sqrt3)$
Option 2: $36\sqrt3$
Option 3: $360$
Option 4: $72(5+\sqrt3)$
Question : The perimeter of an isosceles triangle is 544 cm and each of the equal sides is $\frac{5}{6}$ times the base. What is the area (in cm2) of the triangle?
Option 1: 38172
Option 2: 18372
Option 3: 31872
Option 4: 13872
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile