A builder wants to create a rectangular room in a house she wants it to have a total area of 375 square feet, and it should be 10 feet longer than it is wide

Width = 15 ft

Length = 25ft

Step-by-step explanation:

Given that:

Total area = 375 ft²

Length = 10 + width

Let ;

Width = x

Length = x + 10

Area of a rectangle = Length * Width

Area of rectangle = 375 ft²

375 = x * (x + 10)

375 = X² + 10x

x² + 10x - 375 = 0

X² + 25x - 15x - 375 =. 0

x(x + 25) - 15(x + 25) = 0

x +. 25 = 0

x - 15 = 0

Hence,

x = - 25 or x = 15

X cannot be negative

Hence, x = 15

Width = 15 ft

Length = x + 10 = 15 + 10 = 25 ft

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.