Answer:
let length be b+5 and breadth be b
given,
perimeter of rectangle=150
or, 2(l+b) =150
or, 2(b+5+b)=150
or, 2b+5=150/2
or, 2b+5=75
or, 2b=70
therefore, b=35m
l=b+5
=35+5
=40m
Given:
Tangent segment MN = 6
External segment NQ = 4
Secant segment NP =x + 4
To find:
The length of line segment PQ.
Solution:
Property of tangent and secant segment:
If a secant and a tangent intersect outside a circle, then the product of the secant segment and external segment is equal to the product of the tangent segment.
![\Rightarrow NQ\times NP = MN^2](https://tex.z-dn.net/?f=%5CRightarrow%20NQ%5Ctimes%20NP%20%3D%20MN%5E2)
![\Rightarrow 4\times (x+4) = 6^2](https://tex.z-dn.net/?f=%5CRightarrow%204%5Ctimes%20%28x%2B4%29%20%3D%206%5E2)
![\Rightarrow 4x+16 = 36](https://tex.z-dn.net/?f=%5CRightarrow%204x%2B16%20%3D%2036)
Subtract 16 from both sides.
![\Rightarrow 4x+16-16 = 36-16](https://tex.z-dn.net/?f=%5CRightarrow%204x%2B16-16%20%3D%2036-16)
![\Rightarrow 4x =20](https://tex.z-dn.net/?f=%5CRightarrow%204x%20%3D20)
Divide by 4 on both sides.
![$\Rightarrow\frac{4x}{4}=\frac{20}{4}](https://tex.z-dn.net/?f=%24%5CRightarrow%5Cfrac%7B4x%7D%7B4%7D%3D%5Cfrac%7B20%7D%7B4%7D)
![\Rightarrow x = 5](https://tex.z-dn.net/?f=%5CRightarrow%20x%20%3D%205)
The length of line segment PQ is 5 units.
Answer:
c
Step-by-step explanation:
The area is 3/8 yd².
Area = length x width
Given:
length = 3/4 yard
width = 1/2 yard
Area = 3/4 yd * 1/2 yd
Area = 3*1/4*2
Area = 3/8 yd²
In multiplying fractions, multiply the numerators, then, multiply the denominators. lastly, simplify the fraction. 3/8 yd² is already in its simplest form.