Answer:
Base = 24 cm or 10cm
Step-by-step explanation:
REMEMBER:
An isosceles triangle ABC with base BC = ‘b' & height AD = ‘h' & its equal sides =13 cm & area = 60 cm²
Using the formulas


There are 2 solutions for 
≈ 
Less complex:
Area of a triangle = 1/2 * b * h = 60
=> h = 120/b
In right triangle ABD
13² = h² + b² /4 ( by Pythagoras law)
=>169 = 120²/b² + b²/4
=>676 b² = 57600 + b^4
=> b^4 - 676 b² + 57600 = 0
=> b² = 676 +- √(676² - 4*57600) / 2
=> b²= 676 +- √(226576) /2
=> b² = (676 +- 476 )/2
=> b² = 1152/2 , 200 /2
=> b² = 576 , 100
=> b = 24, 10
So, Base = 24 cm or 10cm
we know that
Vertical angles are congruent angles
that means
substitute the given values
(7x – 27)=(3x + 29)
solve for x
7x-3x=29+27
4x=56
x=14
part b)
We know that
Supplementary angles are angles that their sum is equal to 180 degrees
so
A+B=180
substitute the given values
5x+25+x+17=180
solve for x
6x+42=180
6x=180-42
6x=138
x=23
Find the measure of Angle A
D)A rectangle is always also a parallelogram.