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In Triangle QRS, A is the midpoint of QR, B is the midpoint of RS, and C is the midpoint of SQ.
Also, QA = 10, BR = 15, and SQ = 28.
What is the perimeter of the Triangle ABC?

Answer 1

39 units

Explanation :

given to us is a triangle QRS with A as the midpoint of QR ,B as the midpoint of RS and C as the midpoint of SQ. we know that midpoint divides the segment into two equal part thus,

• QA = AR
• BR = BS
• CQ = CS

which also means that each part of the segment would be the half of the whole measure of the segment thus,

• QA = AR = 10
• BR = BS = 15
• CQ = CS = 28/2 = 14

ATQ,

ΔABC is made up by adjoining the midpoints to each other,thus , we can find it's perimeter using the midpoint theorem which states that the line segment which adjoins the midpoint of either of the two sides of the respective triangle is ll to the third side and it's measure is half of that of the third side .

thus,

• AB = 1/2 SQ = 14
• BC = 1/2 QR = 10
• CA = 1/2 RS = 15

hence,the perimeter of ΔABC would be

• AB + BC + CA = 14 + 10 + 15 = 39 units

therefore,the required perimeter is 39 units.