The altitude drawn to the base of an isosceles triangle is 8cm and the perimeter

CuriousTab

CuriousTab

Home Aptitude

Discussion

Home ‣ Aptitude ‣ Area See What Others Are Saying!

Question
The altitude drawn to the base of an isosceles triangle is 8cm and the perimeter is 32cm. Find the area of the triangle?
Options
A. 50
B. 60
C. 70
D. 80

Correct Answer

60

Explanation

let ABC be the isosceles triangle, the AD be the altitude

Let AB = AC = x then BC= 32-2x [because parameter = 2 (side) + Base]

since in an isoceles triange the altitude bisects the base so

BD = DC = 16-x

In a triangle ADC, ${(A C)}^{2} = {(A D)}^{2} + {(D C)}^{2}$

$x^{2} = 8^{2} + {(16 - x)}^{2}$ $? x = 10$

BC = 32-2x = 32-20 = 12 cm

Hence, required area = $\frac{1}{2} * B C * A D$ = $\frac{1}{2} * 12 * 10$ = 60 sq cm

Tags:

More questions

2.
If U = {a, b, c, d, e, f}, A = {a, b, c}, find (U ? A)?.
Options
A. U
B. A
C. ?
D. None of these

3.
Mukul's income is 10% more than Sunil's. How much less is Sunil's income than that of Mukul's?
Options
A. 8.09 %
B. 9.09 %
C. 7.09 %
D. 7.90 %

6. If the number 481 * 673 is completely divisible by 9, then the smallest whole number in place of * will be:
Options
A. 2
B. 5
C. 6
D. 7
E. None of these

8.
The true discount on a certain bill due for nine months at 4 % simple interest is ?150. Find the amount of the bill.
Options
A. ?5150
B. ?5250
C. ?4750
D. ?5650

9.
The present worth of $ 220.50 due in 2 years reckoning compound interest at 5 % is :
Options
A. $ 200
B. $ 197.5
C. $ 202
D. $ 192.25

Comments

More in Aptitude: