Find the missing side length of the triangular prism

Question

The surface area is 510 cm^2

We need to find the length

the right triangle has a base of 5cm and a height of 12 cm

The triangles longest side is 13cm. What is the length of the base of the prism

Answer 1

Since we cannot draw shapes,

Sides Top and Bottom

Surface Area = (5 + 12 + 13) X + 2(5 x 12)/2 = 510

Length of the base X = 15 cm

Answer 2

Right Triangular Prism

A right triangular prism is a prism with two parallel and congruent triangular faces and three rectangular faces perpendicular to the triangular ones. (If the lateral faces are not perpendicular to the bases, that is a plain triangular prism.) This is a polyhedron with 6 vertices, 9 edges, and 5 faces. If the triangular faces are equilateral, the prism is regular, in which case the rectangular faces are congruent.

............see diagram in comments section......................

Find the missing side length of the triangular prism

The surface area is 510 cm^2

We need to find the length

the right triangle has a base of 5cm and a height of 12 cm

The triangles longest side is 13cm. What is the length of the base of the prism

The surface area of a right triangular prism is bh+(s₁ + s₂ + h)L

SA = 5cm × 12cm + (5cm + 13cm + 12cm) × L

or.....

510 cm² = 60cm² + (30cm x L)

............solve for L......

450 = 30L

L = 15 cm

...check....

SA = 5cm × 12cm + (5cm + 13cm + 12cm) × 15cm

= 60cm² + (30 cm x15cm)

= 60cm² + 450 cm²

= 510 cm².....that checks out perfectly....any questions???

Diagram borrowed and adapted for this problem from the site below....

https://www.cuemath.com/measurement/surface-area-of-a-right-triangular-prism/