The base of a triangle is 10 inches more than 3 times the height. if the area of the triangle is 16 square inches, find the base and the height

Let h represent the height of the triangle.

... b = 10 + 3h . . . . . . the base is 10 inches more than 3 times the height

... A = (1/2)bh . . . . . . formula for the area of a triangle in terms of base and height

... 16 = (1/2)(10 +3h)h . . . . substitute the known values

... 3h² + 10h - 32 = 0 . . . . rearrange to standard form

... (h -2)(3h +16) = 0

... h = 2 or -16/3 . . . . . . . . the negative solution is extraneous

... b = 10 + 3·2 = 16 . . . . . use the relation between b and h

The base and height of the triangle are 2 inches and 16 inches, respectively.

27 inches

Step-by-step explanation:

To find the length of the diagonal, we just need to use the cosine relation of the 48° angle.

The adjacent side to the angle is the height of the canvas, and the hypotenuse formed is the diagonal of the canvas. So, we have that:

cos(48) = height / diagonal

0.6691 = 18 / diagonal

diagonal = 18 / 0.6691 = 26.9 inches

Rounding to the nearest inch, the diagonal of the canvas measures 27 inches