The length of a rectangle is four times its width. if the area of the rectangle is 100 cm2 , find its perimeter.

1 answer:

7 0

Define x:
Let the width be x.
width = x
Length = 4x

Given the area, find Length and Width:
The area is 100 cm²

Area = Length x Width
x(4x) = 100

Evaluate the Left Hand Side:
4x² = 100

Divide by 4:
x² = 25

Square root both sides:
x = 5

Find the Width and the Length:
Width = x = 5
Length = 4x = 4(5) = 20

Find Perimeter:
Perimeter = 2( 5 + 20) = 50 m

Answer: Perimeter = 50 m

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Answer:

74.0°

Step-by-step explanation:

In triangle JKL, k = 4.1 cm, j = 3.8 cm and ∠J=63°. Find all possible values of angle K, to the nearest 10th of a degree

Solution:

A triangle is a polygon with three sides and three angles. Types of triangles are right angled triangle, scalene triangle, equilateral triangle and isosceles triangle.

Given a triangle with angles A, B, C and the corresponding sides opposite to the angles as a, b, c. Sine rule states that for the triangle, the following holds:

$\frac{a}{sin(A)}=\frac{b}{sin(B)}=\frac{c}{sin(C)}$

In triangle JKL, k=4.1 cm, j=3.8 cm and angle J=63°.

Using sine rule, we can find ∠K:

$\frac{k}{sin(K)}=\frac{j}{sin(J)} \\\\\frac{4.1}{sin(K)}=\frac{3.8}{sin(63)} \\\\sin(K)=\frac{4.1*sin(63)}{3.8}\\\\sin(K)=0.9613\\\\K=sin^{-1} (0.9613)\\\\K=74.0^o \\$