Answer:
Step-by-step explanation:
The quadrilateral has 4 sides and only two of them are equal.
A) to find PR, we will consider the triangle, PRQ.
Using cosine rule
a^2 = b^2 + c^2 - 2abcos A
We are looking for PR
PR^2 = 8^2 + 7^2 - 2 ×8 × 7Cos70
PR^2 = 64 + 49 - 112 × 0.3420
PR^2 = 113 - 38.304 = 74.696
PR = √74.696 = 8.64
B) to find the perimeter of PQRS, we will consider the triangle, RSP. It is an isosceles triangle. Therefore, two sides and two base angles are equal. To determine the length of SP,
We will use the sine rule because only one side,PR is known
For sine rule,
a/sinA = b/sinB
SP/ sin 35 = 8.64/sin110
Cross multiplying
SPsin110 = 8.64sin35
SP = 8.64sin35/sin110
SP = (8.64 × 0.5736)/0.9397
SP = 5.27
SR = SP = 5.27
The perimeter of the quadrilateral PQRS is the sum of the sides. The perimeter = 8 + 7 + 5.27 + 5.27 = 25.54 cm
Yes, because 24^2 is 576 and 10^2 is 100. Together, its 676. And the square root of 26 is 676. So, yes it is a right triangle.
<em>See</em><em> </em><em>above</em><em> </em><em>graph</em>
I am joyous to assist you anytime.
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