Answer:
The length of KS is 25 units and the length of KP is 17 units.
Step-by-step explanation:
Given information: KPST is a trapezoid, KP=ST, MN is a mid segment, MN=20, h=15, PS:KT=3:7 .
Since two sides of the trapezoid are equal therefore it is an isosceles trapezoid.
The midsegment of a trapezoid is a line segment which connects the midpoints of the non-parallel sides.
The length of mid segment is average of length of parallel lines. The length of mid segment is 20.
It is given that PS:KT=3:7. Let the length of sides be 3x and 7x respectively.
[tex]\frac{3x+7x}{2}=20[/tex]
[tex]\frac{10x}{2}=20[/tex]
[tex]5x=20[/tex]
[tex]x=4[/tex]
The value of 3x and 7x are 12 and 28 respectively. So, the length of sides PS and KT is 12 and 28 respectively.
Use pythagoras in triangle AKP.
[tex]AK^2+AP^2=KP^2[/tex]
[tex](8)^2+(15)^2=KP^2[/tex]
[tex]\sqrt{64+225}=KP[/tex]
tex]\sqrt{289}=KP[/tex]
[tex]17=KP[/tex]
Use pythagoras in triangle BKS.
[tex]BK^2+BS^2=KS^2[/tex]
[tex](20)^2+(15)^2=KS^2[/tex]
[tex]\sqrt{400+225}=KS[/tex]
tex]\sqrt{625}=KS[/tex]
[tex]KS=25[/tex]
Therefore length of KS is 25 units and the length of KP is 17 units.
