A triangle and a rectangle are shown below.

Triangle height is 8cm, base is 6cm
Rectangle length is 12cm

The area of the rectangle is 5 times the area of the triangle.

Work out the width (w) of the rectangle.

The Width = 10cm

Step-by-step explanation:

Area of Triangle = 1/2 × base × height

Area of rectangle = Length × Width

Area of Triangle = 1/2 × 6 × 8 = 24cm^2

From the question:

Area of rectangle = 5 times area of triangle

L × W = 5 × 24

12 × W = 120

12W/12 = 120/12

W = 10cm

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).

77

step-by-step explanation: