Answer:
Length of KS = 25 units and
Length of KP = 17 units.
Step-by-step explanation:
Given: KPST is a trapezoid, KP =ST, MN is a mid segment, h is the height =15
Also it is given that, MN = 20 , h = 15 and PS:KT = 3:7.
- If two sides of the trapezoid are equal then, it is an isosceles trapezoid.
- Mid-segment of a trapezoid is a line segment which connects the midpoints of the non-parallel sides.
- A trapezoid mid segment connects the midpoints of two congruent sides of the trapezoid and is parallel to the pair of parallel sides.
- Length of the mid segment is the sum of two bases divide by 2
Since, the length of Mid-segment MN = 20.
Also, it is given: PS:KT = 3:7
Let PS = 3x and KT = 7x respectively.
then;
On Simplify, we get;
5x =20
Divide both sides by 5 we get;
x =4
Then:
Length of base PS = 3x = 3(4) = 12 and Length of base KT = 7x = 7(4) = 28.
Now, In triangle PLK
Using Pythagoras theorem to find KP;
It is given here, PL =h =15 and KL= 8 {you can see in the figure as shown below};
Simplify:
KP = 17
therefore, the length KP = 17 units
To, construct a line: Join K and S
Now, in triangle KRS
KR = KL +LR = 8 +12 =20 and SR = h= 15
Using Pythagoras theorem in KRS to find KS;
On simplify:
KS = 25
Therefore, the length of KS is, 25 units.
